Hydrophobic collapse in (in silico) protein folding

A model of hydrophobic collapse, which is treated as the driving force for protein folding, is presented. This model is the superposition of three models commonly used in protein structure prediction: (1) 'oil-drop' model introduced by Kauzmann, (2) a lattice model introduced to decrease the number of degrees of freedom for structural changes and (3) a model of the formation of hydrophobic core as a key feature in driving the folding of proteins. These three models together helped to develop the idea of a fuzzy-oil-drop as a model for an external force field of hydrophobic character mimicking the hydrophobicity-differentiated environment for hydrophobic collapse. All amino acids in the polypeptide interact pair-wise during the folding process (energy minimization procedure) and interact with the external hydrophobic force field defined by a three-dimensional Gaussian function. The value of the Gaussian function usually interpreted as a probability distribution is treated as a normalized hydrophobicity distribution, with its maximum in the center of the ellipsoid and decreasing proportionally with the distance versus the center. The fuzzy-oil-drop is elastic and changes its shape and size during the simulated folding procedure.

[1]  K A Dill,et al.  A simple model of chaperonin‐mediated protein folding , 1996, Proteins.

[2]  E I Shakhnovich,et al.  A test of lattice protein folding algorithms. , 1995, Proceedings of the National Academy of Sciences of the United States of America.

[3]  G. Rose,et al.  Hydrophobicity of amino acid residues in globular proteins. , 1985, Science.

[4]  D. Baker,et al.  Prediction of local structure in proteins using a library of sequence-structure motifs. , 1998, Journal of molecular biology.

[5]  E I Shakhnovich,et al.  Specific nucleus as the transition state for protein folding: evidence from the lattice model. , 1994, Biochemistry.

[6]  Y. Amemiya,et al.  The compactness of ribonuclease A and reduced ribonuclease A , 1998, FEBS letters.

[7]  A. Garcia,et al.  Simulations of the pressure and temperature unfolding of an α-helical peptide , 2005 .

[8]  N. Go,et al.  Studies on protein folding, unfolding and fluctuations by computer simulation. I. The effect of specific amino acid sequence represented by specific inter-unit interactions. , 2009 .

[9]  A. Fersht,et al.  Effects of heme on the structure of the denatured state and folding kinetics of cytochrome b562. , 2005, Journal of molecular biology.

[10]  Leszek Konieczny,et al.  Conformational subspace in simulation of early‐stage protein folding , 2004, Proteins.

[11]  J. Trewhella,et al.  Denatured states of ribonuclease A have compact dimensions and residual secondary structure. , 1992, Biochemistry.

[12]  I. Tavernelli,et al.  Dynamics of RNase-A and S-protein: a molecular dynamics simulation of the transition toward a folding intermediate. , 2003, Biophysical journal.

[13]  H. Scheraga,et al.  Two new structured intermediates in the oxidative folding of RNase A , 1999, FEBS letters.

[14]  MICHAŁ BRYLIŃSKI,et al.  LIMITATION OF CONFORMATIONAL SPACE FOR PROTEINS – EARLY STAGE FOLDING SIMULATION OF HUMAN α AND β HEMOGLOBIN , 2004 .

[15]  Zbyszek Otwinowski,et al.  The crystal structure of the bacterial chaperonln GroEL at 2.8 Å , 1994, Nature.

[16]  Frances M. G. Pearl,et al.  The CATH Domain Structure Database and related resources Gene3D and DHS provide comprehensive domain family information for genome analysis , 2004, Nucleic Acids Res..

[17]  J L Finney,et al.  Molecular and mesoscale structures in hydrophobically driven aqueous solutions. , 2003, Biophysical chemistry.

[18]  Harold A. Scheraga,et al.  Energy parameters in polypeptides. 8. Empirical potential energy algorithm for the conformational analysis of large molecules , 1978 .

[19]  H. Scheraga,et al.  Regeneration of three-disulfide mutants of bovine pancreatic ribonuclease A missing the 65-72 disulfide bond: characterization of a minor folding pathway of ribonuclease A and kinetic roles of Cys65 and Cys72. , 1998, Biochemistry.

[20]  A. Garcia,et al.  Helix‐coil transition of alanine peptides in water: Force field dependence on the folded and unfolded structures , 2005, Proteins.

[21]  David C. Jones,et al.  CATH--a hierarchic classification of protein domain structures. , 1997, Structure.

[22]  David A. Case,et al.  Effective Born radii in the generalized Born approximation: The importance of being perfect , 2002, J. Comput. Chem..

[23]  B. Rost,et al.  Redefining the goals of protein secondary structure prediction. , 1994, Journal of molecular biology.

[24]  I Roterman,et al.  Modelling the optimal simulation path in the peptide chain folding--studies based on geometry of alanine heptapeptide. , 1995, Journal of theoretical biology.

[25]  Richard Bonneau,et al.  Improving the performance of rosetta using multiple sequence alignment information and global measures of hydrophobic core formation , 2001, Proteins.

[26]  C. Orengo,et al.  Analysis and assessment of ab initio three‐dimensional prediction, secondary structure, and contacts prediction , 1999, Proteins.

[27]  C. Dobson.  The structural basis of protein folding and its links with human disease. , 2001, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[28]  A. Horwich,et al.  The crystal structure of the asymmetric GroEL–GroES–(ADP)7 chaperonin complex , 1997, Nature.

[29]  H. Scheraga,et al.  Energy parameters in polypeptides. 9. Updating of geometrical parameters, nonbonded interactions, and hydrogen bond interactions for the naturally occurring amino acids , 1983 .

[30]  D Baker,et al.  Global properties of the mapping between local amino acid sequence and local structure in proteins. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[31]  C. Etchebest,et al.  Bayesian probabilistic approach for predicting backbone structures in terms of protein blocks , 2000, Proteins.

[32]  A. Horwich,et al.  Chaperone rings in protein folding and degradation. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[33]  Leszek Konieczny,et al.  Early-Stage Folding in Proteins (In Silico) Sequence-to-Structure Relation , 2005, Journal of biomedicine & biotechnology.

[34]  H. Valadié,et al.  Extension of a local backbone description using a structural alphabet: A new approach to the sequence‐structure relationship , 2002, Protein science : a publication of the Protein Society.

[35]  Peter A. Kollman,et al.  AMBER, a package of computer programs for applying molecular mechanics, normal mode analysis, molecular dynamics and free energy calculations to simulate the structural and energetic properties of molecules , 1995 .

[36]  L. Gierasch,et al.  Basis of substrate binding by the chaperonin GroEL. , 1999, Biochemistry.

[37]  M. Palumbo,et al.  Patterns, structures, and amino acid frequencies in structural building blocks, a protein secondary structure classification scheme , 1997, Proteins.

[38]  R. L. Baldwin,et al.  Making a Network of Hydrophobic Clusters , 2002, Science.

[39]  K Schulten,et al.  VMD: visual molecular dynamics. , 1996, Journal of molecular graphics.

[40]  H. Taguchi,et al.  On the Maximum Size of Proteins to Stay and Fold in the Cavity of GroEL underneath GroES* , 1999, The Journal of Biological Chemistry.

[41]  J. Janin,et al.  Surface and inside volumes in globular proteins , 1979, Nature.

[42]  S Roy,et al.  Hydrophobic basis of packing in globular proteins. , 1980, Proceedings of the National Academy of Sciences of the United States of America.

[43]  W. Kauzmann.  Some factors in the interpretation of protein denaturation. , 1959, Advances in protein chemistry.

[44]  I Roterman,et al.  The geometrical analysis of peptide backbone structure and its local deformations. , 1995, Biochimie.

[45]  T. N. Bhat,et al.  The Protein Data Bank , 2000, Nucleic Acids Res..

[46]  Leszek Konieczny,et al.  Fuzzy-Oil-Drop Hydrophobic Force Field—A Model to Represent Late-stage Folding (In Silico) of Lysozyme , 2006, Journal of biomolecular structure & dynamics.

[47]  H. Scheraga,et al.  Regeneration of bovine pancreatic ribonuclease A: detailed kinetic analysis of two independent folding pathways. , 1998, Biochemistry.

[48]  K. R. Woods,et al.  Prediction of protein antigenic determinants from amino acid sequences. , 1981, Proceedings of the National Academy of Sciences of the United States of America.

[49]  N. Ban,et al.  Trigger factor in complex with the ribosome forms a molecular cradle for nascent proteins , 2004, Nature.

[50]  D. Case,et al.  Generalized born models of macromolecular solvation effects. , 2000, Annual review of physical chemistry.

[51]  G. Petsko,et al.  Effects of temperature on protein structure and dynamics: X-ray crystallographic studies of the protein ribonuclease-A at nine different temperatures from 98 to 320 K. , 1993, Biochemistry.

[52]  B. Rost,et al.  A modified definition of Sov, a segment‐based measure for protein secondary structure prediction assessment , 1999, Proteins.

[53]  S. Rackovsky,et al.  Empirical Studies of Hydrophobicity. 1. Effect of Protein Size on the Hydrophobic Behavior of Amino Acids , 1980 .

[54]  J. Onuchic,et al.  Protein folding funnels: the nature of the transition state ensemble. , 1996, Folding & design.

[55]  L. Wyns,et al.  The structures of rnase a complexed with 3′‐CMP and d(CpA): Active site conformation and conserved water molecules , 1994, Protein science : a publication of the Protein Society.

[56]  S. Mande,et al.  Metal ions modulate the plastic nature of Mycobacterium tuberculosis chaperonin-10. , 2001, Protein engineering.

[57]  T. Steitz,et al.  Identifying nonpolar transbilayer helices in amino acid sequences of membrane proteins. , 1986, Annual review of biophysics and biophysical chemistry.

[58]  D. Yee,et al.  Principles of protein folding — A perspective from simple exact models , 1995, Protein science : a publication of the Protein Society.

[59]  J. King,et al.  Frequencies of amino acid strings in globular protein sequences indicate suppression of blocks of consecutive hydrophobic residues , 2001, Protein science : a publication of the Protein Society.

[60]  C. Chothia.  Structural invariants in protein folding , 1975, Nature.

[61]  C. Pace,et al.  Forces contributing to the conformational stability of proteins , 1996, FASEB journal : official publication of the Federation of American Societies for Experimental Biology.

[62]  H. Scheraga,et al.  Empirical Studies of Hydrophobicity. 2. Distribution of the Hydrophobic, Hydrophilic, Neutral, and Ambivalent Amino Acids in the Interior and Exterior Layers of Native Proteins , 1980 .

[63]  James E. Bray,et al.  Assigning genomic sequences to CATH , 2000, Nucleic Acids Res..

[64]  H. H. Rosenbrock,et al.  An Automatic Method for Finding the Greatest or Least Value of a Function , 1960, Comput. J..

[65]  B. Rost,et al.  Prediction of protein secondary structure at better than 70% accuracy. , 1993, Journal of molecular biology.

[66]  K Nishikawa,et al.  Strong hydrophobic nature of cysteine residues in proteins , 1999, FEBS letters.

[67]  R. Doolittle,et al.  A simple method for displaying the hydropathic character of a protein. , 1982, Journal of molecular biology.

[68]  S Gnanakaran,et al.  Simulations of the pressure and temperature unfolding of an alpha-helical peptide. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[69]  C. Tanford.  Protein denaturation. , 1968, Advances in protein chemistry.

[70]  Dominik Gront,et al.  A simple lattice model that exhibits a protein-like cooperative all-or-none folding transition. , 2003, Biopolymers.

[71]  A Kolinski,et al.  Dynamic Monte Carlo simulations of a new lattice model of globular protein folding, structure and dynamics. , 1991, Journal of molecular biology.

[72]  Irena Roterman-Konieczna,et al.  Limited conformational space for early-stage protein folding simulation , 2004, Bioinform..

[73]  Irena Roterman-Konieczna,et al.  SPI - Structure predictability index for protein sequences , 2004, Silico Biol..

[74]  N. Kurochkina,et al.  Heterogeneity of packing: Structural approach , 1998, Protein science : a publication of the Protein Society.

[75]  Oleg V. Tsodikov,et al.  Novel computer program for fast exact calculation of accessible and molecular surface areas and average surface curvature , 2002, J. Comput. Chem..

[76]  H. Scheraga,et al.  Energy parameters in polypeptides. 10. Improved geometrical parameters and nonbonded interactions for use in the ECEPP/3 algorithm, with application to proline-containing peptides , 1994 .

[77]  Irena Roterman-Konieczna,et al.  Gauss-Function-Based Model of Hydrophobicity Density in Proteins , 2006, Silico Biol..

[78]  I M Klotz,et al.  Comparison of molecular structures of proteins: helix content; distribution of apolar residues. , 1970, Archives of biochemistry and biophysics.

[79]  M. Karplus,et al.  Kinetics of protein folding. A lattice model study of the requirements for folding to the native state. , 1994, Journal of molecular biology.

[80]  J. Skolnick,et al.  Monte carlo simulations of protein folding. I. Lattice model and interaction scheme , 1994, Proteins.

[81]  Junmei Wang,et al.  How well does a restrained electrostatic potential (RESP) model perform in calculating conformational energies of organic and biological molecules? , 2000, J. Comput. Chem..

[82]  Leszek Konieczny,et al.  Hydrophobic collapse in late-stage folding (in silico) of bovine pancreatic trypsin inhibitor. , 2006, Biochimie.

[83]  M. Klapper,et al.  On the nature of the protein interior. , 1971, Biochimica et biophysica acta.

[84]  D. Eisenberg,et al.  Analysis of membrane and surface protein sequences with the hydrophobic moment plot. , 1984, Journal of molecular biology.

[85]  H. Scheraga,et al.  Energy parameters in polypeptides. VII. Geometric parameters, partial atomic charges, nonbonded interactions, hydrogen bond interactions, and intrinsic torsional potentials for the naturally occurring amino acids , 1975 .

[86]  Leszek Konieczny,et al.  Limitation of conformational space for proteins -- early stage folding simulation of human alpha and beta hemoglobin chains , 2004 .

[87]  K. Dill.  Dominant forces in protein folding. , 1990, Biochemistry.

[88]  H. Scheraga,et al.  Empirical studies of hydrophobicity. 3. Radial distribution of clusters of hydrophobic and hydrophilic amino acids , 1981 .

[89]  H. Scheraga,et al.  Intermolecular potentials from crystal data. 6. Determination of empirical potentials for O-H...O = C hydrogen bonds from packing configurations , 1984 .

[90]  V S Pande,et al.  Folding pathway of a lattice model for proteins. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[91]  Dmitrij Frishman,et al.  Identification of in vivo substrates of the chaperonin GroEL , 1999, Nature.

[92]  M. Levitt.  A simplified representation of protein conformations for rapid simulation of protein folding. , 1976, Journal of molecular biology.

[93]  A. Ravve,et al.  Principles of Polymer Chemistry , 1995 .

[94]  S. I. Rogov,et al.  A numerical measure of amino acid residues similarity based on the analysis of their surroundings in natural protein sequences. , 2001, Protein engineering.

[95]  I Roterman,et al.  Lysozyme Folded In Silico According to the Limited Conformational Sub-space , 2004, Journal of biomolecular structure & dynamics.